geophys (version 1.2-1)

PolarDecomp: Polar Decomposition

Description

Polar Decomposition for Strain

Usage

PolarDecomp(A)

Arguments

A

Strain Matrix

Value

• P
  matrix, stretch tensor
• U
  matrix, orthogonal rotation matrix

Details

Polar decomposition uses the svd to extract 2 matrices that represent the stretch and rotation of a strain: A = UP. U is orthogonal rotation matrix and P is the stretch tensor. These are extracted from the singular value decomposition.

References

http://en.wikipedia.org/wiki/Finite_strain_theory

See Also

svd

Examples

A = matrix(runif(4, -1, 1), ncol=2)
PD = PolarDecomp(A)

E = svd(A)

###  W         S           V
 E$u
 ###t(E$v) %*% diag(E$d)%*%  (E$u)

P = E$vU =  E$u

U